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输出：[[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [0]
输出：[[],[0]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= nums.length &lt;= 10</code></li> <li><code>-10 &lt;= nums[i] &lt;= 10</code></li> <li><code>nums</code> 中的所有元素 <strong>互不相同</strong></li></ul> <h5 id="完整代码"><a href="#完整代码" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number[]} nums
 * @return {number[][]}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">subsets</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">nums</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 对于子集，其实就是每个元素选不选的问题</span>

    <span class="token comment">// 0 不选</span>
    <span class="token comment">// 1 选</span>

    <span class="token comment">// 对于[1,2,3]</span>
    <span class="token comment">// 0 0 0 []</span>
    
    <span class="token comment">// [0,1],[0,1],[0,1]</span>


    <span class="token comment">// let index=0</span>
    <span class="token keyword">var</span> res1<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>

    <span class="token keyword">let</span> temp<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>

    <span class="token comment">// 不管当前元素选或者不选，是不是都要走到下一层</span>
    <span class="token keyword">const</span> <span class="token function-variable function">findSubSet</span><span class="token operator">=</span><span class="token punctuation">(</span><span class="token parameter">temp<span class="token punctuation">,</span>index</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>
        <span class="token comment">// console.log(temp,index)</span>

        <span class="token keyword">if</span><span class="token punctuation">(</span>index<span class="token operator">===</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token punctuation">{</span>
            console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>temp<span class="token punctuation">,</span>index<span class="token punctuation">)</span>
            res1<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>Array<span class="token punctuation">.</span><span class="token function">from</span><span class="token punctuation">(</span>temp<span class="token punctuation">)</span><span class="token punctuation">)</span>
            <span class="token keyword">return</span> 
        <span class="token punctuation">}</span>
        <span class="token comment">// 不选</span>
        <span class="token function">findSubSet</span><span class="token punctuation">(</span>temp<span class="token punctuation">,</span>index<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span>
        <span class="token comment">// 选</span>
        temp<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>nums<span class="token punctuation">[</span>index<span class="token punctuation">]</span><span class="token punctuation">)</span>
        <span class="token function">findSubSet</span><span class="token punctuation">(</span>temp<span class="token punctuation">,</span>index<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span>
        temp<span class="token punctuation">.</span><span class="token function">pop</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
    <span class="token punctuation">}</span>

    

    <span class="token function">findSubSet</span><span class="token punctuation">(</span>temp<span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">)</span>

    <span class="token keyword">return</span> res1

<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br></div></div><ul><li>注意点：
<ul><li>==选或者不选其实是一个背包问题，即背包容量有限的情况下，如何取舍不同的物品==</li></ul></li></ul> <h4 id="_77-组合-上题的特例"><a href="#_77-组合-上题的特例" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/combinations/" target="_blank" rel="noopener noreferrer">77. 组合(上题的特例)<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给定两个整数 <code>n</code> 和 <code>k</code>，返回范围 <code>[1, n]</code> 中所有可能的 <code>k</code> 个数的组合。</p> <p>你可以按 <strong>任何顺序</strong> 返回答案。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：n = 4, k = 2
输出：
[
  [2,4],
  [3,4],
  [2,3],
  [1,2],
  [1,3],
  [1,4],
]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：n = 1, k = 1
输出：[[1]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= n &lt;= 20</code></li> <li><code>1 &lt;= k &lt;= n</code></li></ul> <h5 id="解题思路"><a href="#解题思路" class="header-anchor">#</a> 解题思路</h5> <div class="language-shell line-numbers-mode"><pre class="language-shell"><code><span class="token number">1</span>.还是子集问题，不过子集的个数有限制，为k
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br></div></div><h5 id="完整代码-2"><a href="#完整代码-2" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number} n
 * @param {number} k
 * @return {number[][]}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">combine</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">n<span class="token punctuation">,</span> k</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token keyword">let</span> s<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>
    <span class="token keyword">let</span> res<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>

    
    <span class="token keyword">const</span> <span class="token function-variable function">findSubSet</span><span class="token operator">=</span><span class="token punctuation">(</span><span class="token parameter">index</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>

        <span class="token comment">// 去除不满满足条件的</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>s<span class="token punctuation">.</span>length<span class="token operator">&gt;</span>k<span class="token operator">||</span>s<span class="token punctuation">.</span>length<span class="token operator">+</span>n<span class="token operator">-</span>index<span class="token operator">+</span><span class="token number">1</span><span class="token operator">&lt;</span>k<span class="token punctuation">)</span><span class="token punctuation">{</span>

            <span class="token comment">// 说明子集长度大于k，或者子集的长度+后面的层数都不足以达到k</span>
            <span class="token keyword">return</span> 
        <span class="token punctuation">}</span>

        <span class="token comment">// 递归出口</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>index<span class="token operator">===</span>n<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
            res<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>Array<span class="token punctuation">.</span><span class="token function">from</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span><span class="token punctuation">)</span>
            <span class="token keyword">return</span> 
        <span class="token punctuation">}</span>

        <span class="token comment">// 对于每一个index，选或者不选</span>

        <span class="token comment">// 不选</span>
        <span class="token function">findSubSet</span><span class="token punctuation">(</span>index<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span>

        <span class="token comment">// 选</span>
        s<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>index<span class="token punctuation">)</span>
        <span class="token function">findSubSet</span><span class="token punctuation">(</span>index<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span>
        s<span class="token punctuation">.</span><span class="token function">pop</span><span class="token punctuation">(</span>index<span class="token punctuation">)</span>
    <span class="token punctuation">}</span>

    <span class="token function">findSubSet</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>

    <span class="token keyword">return</span> res
<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br></div></div><h4 id="_46-全排列-模板题"><a href="#_46-全排列-模板题" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/permutations/description/" target="_blank" rel="noopener noreferrer">46. 全排列(模板题)<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给定一个不含重复数字的数组 <code>nums</code> ，返回其 <em>所有可能的全排列</em> 。你可以 <strong>按任意顺序</strong> 返回答案。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [1,2,3]
输出：[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [0,1]
输出：[[0,1],[1,0]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 3：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [1]
输出：[[1]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= nums.length &lt;= 6</code></li> <li><code>-10 &lt;= nums[i] &lt;= 10</code></li> <li><code>nums</code> 中的所有整数 <strong>互不相同</strong></li></ul> <h5 id="解题思路-2"><a href="#解题思路-2" class="header-anchor">#</a> 解题思路</h5> <div class="language-shell line-numbers-mode"><pre class="language-shell"><code><span class="token number">1</span>. 递归+visited数组，
<span class="token number">2</span>. 每次都选，没有不选的选项
<span class="token number">3</span>. 选择是有限制，已经选过的不能在选择
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><h5 id="完整代码-3"><a href="#完整代码-3" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number[]} nums
 * @return {number[][]}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">permute</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">nums</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 1，2，3 的排列，如果不考虑重复的元素 总数为3*3*3</span>

    <span class="token comment">// 因为不能出现重复的元素，所以会出现死路（不符合条件）和生路（符合条）两种</span>

    <span class="token comment">// 对于这种路很多的情况，一般需要使用递归来解决</span>

    <span class="token keyword">let</span> res<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>

    <span class="token comment">// 定义一个递归的算法</span>
    <span class="token comment">// let path=[]</span>
    <span class="token keyword">const</span> <span class="token function-variable function">backTrack</span><span class="token operator">=</span><span class="token punctuation">(</span><span class="token parameter">path</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>
        <span class="token comment">// 判断n是否已经在数组中</span>

        <span class="token keyword">if</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span>length<span class="token operator">===</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token punctuation">{</span>
            <span class="token comment">// console.log(2)</span>
            res<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>path<span class="token punctuation">)</span>
            <span class="token keyword">return</span> 
        <span class="token punctuation">}</span>
        
        nums<span class="token punctuation">.</span><span class="token function">forEach</span><span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token parameter">item</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>
            <span class="token comment">// 每个都选</span>
            <span class="token comment">// 选择条件限制，选过的不能在再选</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">includes</span><span class="token punctuation">(</span>item<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
            <span class="token comment">// console.log(1,n)</span>
                <span class="token keyword">return</span> 
            <span class="token punctuation">}</span>
            <span class="token function">backTrack</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">concat</span><span class="token punctuation">(</span>item<span class="token punctuation">)</span><span class="token punctuation">)</span>
        <span class="token punctuation">}</span><span class="token punctuation">)</span>
    <span class="token punctuation">}</span>

    <span class="token function">backTrack</span><span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
    <span class="token keyword">return</span> res
<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br></div></div><h4 id="_47-全排列-ii"><a href="#_47-全排列-ii" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/permutations-ii/description/" target="_blank" rel="noopener noreferrer">47. 全排列 II<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给定一个可包含重复数字的序列 <code>nums</code> ，<em><strong>按任意顺序</strong></em> 返回所有不重复的全排列。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [1,1,2]
输出：
[[1,1,2],
 [1,2,1],
 [2,1,1]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [1,2,3]
输出：[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= nums.length &lt;= 8</code></li> <li><code>-10 &lt;= nums[i] &lt;= 10</code></li></ul> <h5 id="解题思路-3"><a href="#解题思路-3" class="header-anchor">#</a> 解题思路</h5> <div class="language-shell line-numbers-mode"><pre class="language-shell"><code><span class="token number">1</span>. 和全排列一样
<span class="token number">2</span>. 添加了更多的限制条件<span class="token operator">==</span><span class="token operator">&gt;</span> 不能出现重复的排列（因为元素可以相同）
<span class="token number">3</span>. 解决方法:使用hash表保证排列的唯一
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><h5 id="完整代码-4"><a href="#完整代码-4" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number[]} nums
 * @return {number[][]}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">permuteUnique</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">nums</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 先全排列排出来</span>

    <span class="token comment">// 我们存一个map</span>

    <span class="token comment">// key = “1,1,2&quot; 如果key相同，即has(key) 越过</span>

    <span class="token comment">// 这里三个元素必选，没有不选的选项</span>
    <span class="token keyword">let</span> res<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>

    <span class="token keyword">let</span> map<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Map</span><span class="token punctuation">(</span><span class="token punctuation">)</span>

    <span class="token keyword">let</span> visited<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>
    
    <span class="token keyword">const</span> <span class="token function-variable function">allSort</span><span class="token operator">=</span><span class="token punctuation">(</span><span class="token parameter">temp<span class="token punctuation">,</span>visitedArr</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>

        <span class="token keyword">if</span><span class="token punctuation">(</span>temp<span class="token punctuation">.</span>length<span class="token operator">===</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token punctuation">{</span>
            <span class="token comment">// console.log(temp)</span>
            <span class="token comment">// 判断temp键是否存在</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>map<span class="token punctuation">.</span><span class="token function">has</span><span class="token punctuation">(</span>temp<span class="token punctuation">.</span><span class="token function">join</span><span class="token punctuation">(</span><span class="token string">&quot;,&quot;</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
                map<span class="token punctuation">.</span><span class="token function">set</span><span class="token punctuation">(</span>temp<span class="token punctuation">.</span><span class="token function">join</span><span class="token punctuation">(</span><span class="token string">&quot;,&quot;</span><span class="token punctuation">)</span><span class="token punctuation">,</span>Array<span class="token punctuation">.</span><span class="token function">from</span><span class="token punctuation">(</span>temp<span class="token punctuation">)</span><span class="token punctuation">)</span>
            <span class="token punctuation">}</span>
            <span class="token keyword">return</span> 
        <span class="token punctuation">}</span>

        nums<span class="token punctuation">.</span><span class="token function">forEach</span><span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token parameter">item<span class="token punctuation">,</span>index</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>visitedArr<span class="token punctuation">.</span><span class="token function">includes</span><span class="token punctuation">(</span>index<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
                <span class="token function">allSort</span><span class="token punctuation">(</span>temp<span class="token punctuation">.</span><span class="token function">concat</span><span class="token punctuation">(</span>item<span class="token punctuation">)</span><span class="token punctuation">,</span>visitedArr<span class="token punctuation">.</span><span class="token function">concat</span><span class="token punctuation">(</span>index<span class="token punctuation">)</span><span class="token punctuation">)</span>
            <span class="token punctuation">}</span>
            <span class="token comment">// console.log(index)</span>
            
        <span class="token punctuation">}</span><span class="token punctuation">)</span>

    <span class="token punctuation">}</span>

    <span class="token function">allSort</span><span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">,</span>visited<span class="token punctuation">)</span>

    map<span class="token punctuation">.</span><span class="token function">forEach</span><span class="token punctuation">(</span><span class="token parameter">item</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>
        res<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>item<span class="token punctuation">)</span>
    <span class="token punctuation">}</span><span class="token punctuation">)</span>

    <span class="token keyword">return</span> res
<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br><span class="line-number">47</span><br><span class="line-number">48</span><br></div></div><h4 id="_98-验证二叉搜索树"><a href="#_98-验证二叉搜索树" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/validate-binary-search-tree/description/" target="_blank" rel="noopener noreferrer">98. 验证二叉搜索树<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给你一个二叉树的根节点 <code>root</code> ，判断其是否是一个有效的二叉搜索树。</p> <p><strong>有效</strong> 二叉搜索树定义如下：</p> <ul><li>节点的左子树只包含 <strong>小于</strong> 当前节点的数。</li> <li>节点的右子树只包含 <strong>大于</strong> 当前节点的数。</li> <li>所有左子树和右子树自身必须也是二叉搜索树。</li></ul> <p><strong>示例 1：</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/12/01/tree1.jpg" alt="img"></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：root = [2,1,3]
输出：true
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 2：</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/12/01/tree2.jpg" alt="img"></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：root = [5,1,4,null,null,3,6]
输出：false
解释：根节点的值是 5 ，但是右子节点的值是 4 。
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><p><strong>提示：</strong></p> <ul><li>树中节点数目范围在<code>[1, 104]</code> 内</li> <li><code>-231 &lt;= Node.val &lt;= 231 - 1</code></li></ul> <h5 id="解题思路-4"><a href="#解题思路-4" class="header-anchor">#</a> 解题思路</h5> <div class="language-shell line-numbers-mode"><pre class="language-shell"><code><span class="token number">1</span>. 判断一棵树是否有效<span class="token operator">==</span><span class="token operator">=</span><span class="token operator">&gt;</span>判断其左右子树是否有效
<span class="token number">2</span>. 有效的条件
	左子树中的最大值小于根节点的值
	右子树的最小值大于根节点的值
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br></div></div><h5 id="完整代码-5"><a href="#完整代码-5" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */</span>
<span class="token comment">/**
 * @param {TreeNode} root
 * @return {boolean}
 */</span>

<span class="token comment">// 定义一个数据结构，存储节点数是否有效，即这棵树的最大值和最小值</span>

<span class="token keyword">function</span> <span class="token function">NodeInfo</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>

    <span class="token keyword">this</span><span class="token punctuation">.</span>isValid<span class="token operator">=</span><span class="token boolean">false</span>
    <span class="token keyword">this</span><span class="token punctuation">.</span>maxValue<span class="token operator">=</span><span class="token operator">-</span><span class="token number">Infinity</span>
    <span class="token keyword">this</span><span class="token punctuation">.</span>minValue<span class="token operator">=</span><span class="token number">Infinity</span>
<span class="token punctuation">}</span>

 
<span class="token keyword">var</span> <span class="token function-variable function">isValidBST</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">root</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 有效的判定</span>
    <span class="token comment">// 1. 节点的左子树的最大值left.maxValue&gt;root.val</span>
    <span class="token comment">// 2. 节点的右子树的最小值right.minValue&lt;root.val</span>
    <span class="token comment">// 3. 所有左子树和右子树自身必须也是二叉搜索树</span>


    <span class="token comment">// 定义一个判断子树节点是否满足条件的函数</span>
    <span class="token keyword">const</span> <span class="token function-variable function">checkValid</span><span class="token operator">=</span><span class="token punctuation">(</span><span class="token parameter">root</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>

        <span class="token comment">// 说明节点为空，空节点肯定有效</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>root<span class="token punctuation">)</span><span class="token punctuation">{</span>
            <span class="token keyword">let</span> nodeInfo<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">NodeInfo</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
            nodeInfo<span class="token punctuation">.</span>isValid<span class="token operator">=</span><span class="token boolean">true</span>
            <span class="token keyword">return</span> nodeInfo 
        <span class="token punctuation">}</span>

        <span class="token keyword">let</span> nodeInfo<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">NodeInfo</span><span class="token punctuation">(</span><span class="token punctuation">)</span>

        <span class="token keyword">let</span> leftNode<span class="token operator">=</span><span class="token function">checkValid</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">)</span>
        <span class="token keyword">let</span> rightNode<span class="token operator">=</span><span class="token function">checkValid</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">)</span>

        <span class="token keyword">if</span><span class="token punctuation">(</span>leftNode<span class="token punctuation">.</span>isValid<span class="token operator">&amp;&amp;</span>rightNode<span class="token punctuation">.</span>isValid<span class="token operator">&amp;&amp;</span>leftNode<span class="token punctuation">.</span>maxValue<span class="token operator">&lt;</span>root<span class="token punctuation">.</span>val<span class="token operator">&amp;&amp;</span>rightNode<span class="token punctuation">.</span>minValue<span class="token operator">&gt;</span>root<span class="token punctuation">.</span>val<span class="token punctuation">)</span><span class="token punctuation">{</span>
            nodeInfo<span class="token punctuation">.</span>isValid<span class="token operator">=</span><span class="token boolean">true</span>
        <span class="token punctuation">}</span>

        nodeInfo<span class="token punctuation">.</span>minValue<span class="token operator">=</span>Math<span class="token punctuation">.</span><span class="token function">min</span><span class="token punctuation">(</span>Math<span class="token punctuation">.</span><span class="token function">min</span><span class="token punctuation">(</span>leftNode<span class="token punctuation">.</span>minValue<span class="token punctuation">,</span>rightNode<span class="token punctuation">.</span>minValue<span class="token punctuation">)</span><span class="token punctuation">,</span>root<span class="token punctuation">.</span>val<span class="token punctuation">)</span>
        nodeInfo<span class="token punctuation">.</span>maxValue<span class="token operator">=</span>Math<span class="token punctuation">.</span><span class="token function">max</span><span class="token punctuation">(</span>Math<span class="token punctuation">.</span><span class="token function">max</span><span class="token punctuation">(</span>leftNode<span class="token punctuation">.</span>maxValue<span class="token punctuation">,</span>rightNode<span class="token punctuation">.</span>maxValue<span class="token punctuation">)</span><span class="token punctuation">,</span>root<span class="token punctuation">.</span>val<span class="token punctuation">)</span>

        <span class="token keyword">return</span> nodeInfo
    <span class="token punctuation">}</span>

    <span class="token keyword">let</span> res<span class="token operator">=</span><span class="token function">checkValid</span><span class="token punctuation">(</span>root<span class="token punctuation">)</span>

    console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>res<span class="token punctuation">.</span>isValid<span class="token punctuation">)</span>

    <span class="token keyword">return</span> res<span class="token punctuation">.</span>isValid
<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br><span class="line-number">47</span><br><span class="line-number">48</span><br><span class="line-number">49</span><br><span class="line-number">50</span><br><span class="line-number">51</span><br><span class="line-number">52</span><br><span class="line-number">53</span><br><span class="line-number">54</span><br><span class="line-number">55</span><br><span class="line-number">56</span><br><span class="line-number">57</span><br><span class="line-number">58</span><br><span class="line-number">59</span><br><span class="line-number">60</span><br><span class="line-number">61</span><br><span class="line-number">62</span><br></div></div><h4 id="_50-pow-x-n"><a href="#_50-pow-x-n" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/powx-n/description/" target="_blank" rel="noopener noreferrer">50. Pow(x, n)<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>实现 <a href="https://www.cplusplus.com/reference/valarray/pow/" target="_blank" rel="noopener noreferrer">pow(<em>x</em>, <em>n</em>)<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a> ，即计算 <code>x</code> 的整数 <code>n</code> 次幂函数（即，<code>xn</code> ）。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：x = 2.00000, n = 10
输出：1024.00000
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：x = 2.10000, n = 3
输出：9.26100
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 3：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：x = 2.00000, n = -2
输出：0.25000
解释：2-2 = 1/22 = 1/4 = 0.25
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>-100.0 &lt; x &lt; 100.0</code></li> <li><code>-231 &lt;= n &lt;= 231-1</code></li> <li><code>-104 &lt;= xn &lt;= 104</code></li></ul> <h5 id="完整代码-6"><a href="#完整代码-6" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number} x
 * @param {number} n
 * @return {number}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">myPow</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">x<span class="token punctuation">,</span> n</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// n为偶数时 pow(x,n) pow(x,n/2) *pow(x,n/2)</span>

    <span class="token comment">// n为奇数时 pow(x,n) pow(x,n/2)*pow(x,n/2)*x</span>

    <span class="token comment">// 递归出口 n=0 时 1</span>

    <span class="token comment">// n&lt;0为负数是 pow(x,n) = 1/pow(x,-n)</span>

    console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>n<span class="token punctuation">)</span>


    <span class="token keyword">if</span><span class="token punctuation">(</span>n<span class="token operator">===</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">return</span> <span class="token number">1</span>
    <span class="token punctuation">}</span>

    <span class="token keyword">if</span><span class="token punctuation">(</span>n<span class="token operator">&lt;</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">return</span> <span class="token number">1</span><span class="token operator">/</span><span class="token function">myPow</span><span class="token punctuation">(</span>x<span class="token punctuation">,</span><span class="token operator">-</span>n<span class="token punctuation">)</span>
    <span class="token punctuation">}</span>



    <span class="token keyword">let</span> temp<span class="token operator">=</span><span class="token function">myPow</span><span class="token punctuation">(</span>x<span class="token punctuation">,</span>Math<span class="token punctuation">.</span><span class="token function">floor</span><span class="token punctuation">(</span>n<span class="token operator">/</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">)</span>

    <span class="token keyword">if</span><span class="token punctuation">(</span>n<span class="token operator">%</span><span class="token number">2</span><span class="token operator">===</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">return</span> temp<span class="token operator">*</span>temp
    <span class="token punctuation">}</span><span class="token keyword">else</span> <span class="token keyword">if</span><span class="token punctuation">(</span>n<span class="token operator">%</span><span class="token number">2</span><span class="token operator">===</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">return</span> temp<span class="token operator">*</span>temp<span class="token operator">*</span>x
    <span class="token punctuation">}</span>



<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br></div></div><h4 id="_22-括号生成"><a href="#_22-括号生成" class="header-anchor">#</a> 22. 括号生成</h4> <p>数字 <code>n</code> 代表生成括号的对数，请你设计一个函数，用于能够生成所有可能的并且 <strong>有效的</strong> 括号组合。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：n = 3
输出：[&quot;((()))&quot;,&quot;(()())&quot;,&quot;(())()&quot;,&quot;()(())&quot;,&quot;()()()&quot;]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：n = 1
输出：[&quot;()&quot;]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= n &lt;= 8</code></li></ul> <h5 id="解题思路-5"><a href="#解题思路-5" class="header-anchor">#</a> 解题思路</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token number">1.</span> 括号的组合类型，其实实际情况就两种
<span class="token number">2.</span> <span class="token function">即（）里面套</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token punctuation">,</span><span class="token function">或者</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">...</span><span class="token punctuation">.</span>
<span class="token number">3.</span> 我们把括号组合的问题分为两个子问题
	<span class="token function">一个问题为外层有括号</span> <span class="token punctuation">(</span>a<span class="token punctuation">)</span>
	一个问题为外层没有括号 b<span class="token operator">===</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">...</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br></div></div><h5 id="完整代码-7"><a href="#完整代码-7" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number} n
 * @return {string[]}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">generateParenthesis</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">n</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 递归出口</span>
    <span class="token keyword">if</span><span class="token punctuation">(</span>n<span class="token operator">===</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">return</span> <span class="token punctuation">[</span><span class="token string">&quot;&quot;</span><span class="token punctuation">]</span>
    <span class="token punctuation">}</span>

    <span class="token comment">// 分治解决</span>

    <span class="token comment">// 我们把整体的大括号分为a，b两个子问题</span>

    <span class="token comment">// a 为括号里面内嵌括号的类型 即(  a  ) 其中a为括号组合，也可分为a,b子问题</span>

    <span class="token comment">// b 为单独括号类型，即()*n n&gt;=0  如() ()()  ()()()</span>


    <span class="token comment">// 这么分解，a的外层必定右括号,所有括号个数 1~n</span>


    <span class="token comment">// 类型组合</span>
    <span class="token keyword">let</span> result<span class="token operator">=</span><span class="token punctuation">[</span><span class="token punctuation">]</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">&lt;=</span>n<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token comment">// a类型</span>
        <span class="token comment">// 因为外层括号算一层</span>
        <span class="token keyword">let</span> result_a<span class="token operator">=</span><span class="token function">generateParenthesis</span><span class="token punctuation">(</span>i<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span>

        <span class="token comment">// b类型</span>
        <span class="token keyword">let</span> result_b<span class="token operator">=</span><span class="token function">generateParenthesis</span><span class="token punctuation">(</span>n<span class="token operator">-</span>i<span class="token punctuation">)</span>

        

        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> a <span class="token keyword">of</span> result_a<span class="token punctuation">)</span><span class="token punctuation">{</span>

            <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> b <span class="token keyword">of</span> result_b<span class="token punctuation">)</span><span class="token punctuation">{</span>
                result<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">&quot;(&quot;</span><span class="token operator">+</span>a<span class="token operator">+</span><span class="token string">&quot;)&quot;</span><span class="token operator">+</span>b<span class="token punctuation">)</span>
                
            <span class="token punctuation">}</span>
        <span class="token punctuation">}</span>

    <span class="token punctuation">}</span>

    <span class="token keyword">return</span> result

<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br><span class="line-number">47</span><br><span class="line-number">48</span><br></div></div></div></div>  <div class="page-edit"><div class="edit-link"><a href="https://github.com/linxin1123/vuepress-blog/edit/master/docs/07.算法/41.算法训练营/12.递归-分治.md" target="_blank" rel="noopener noreferrer">编辑</a> <span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></div> <!----> <div class="last-updated"><span class="prefix">上次更新:</span> <span class="time">2023/02/17, 11:29:32</span></div></div> <div class="page-nav-wapper"><div class="page-nav-centre-wrap"><a href="/pages/cf81aa/" class="page-nav-centre page-nav-centre-prev"><div class="tooltip">二叉堆</div></a> <a href="/pages/0e21af/" class="page-nav-centre page-nav-centre-next"><div class="tooltip">深度-广度搜索-状态空间-cnblog</div></a></div> <div class="page-nav"><p class="inner"><span class="prev">
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